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Standard-Form Categorical Syllogisms Syllogism

Categorical syllogisms are deductive arguments with three categorical propositions: two premises and a conclusion. They must be in standard form with the major premise first, then the minor premise, and conclusion last. The middle term appears in both premises but not the conclusion. There are 64 possible moods that a syllogism can take based on whether the propositions are universal or particular affirmatives, negatives, or indefinites. Validity depends on the syllogism's form, not the subject matter. Venn diagrams can help test whether a syllogism is valid or invalid.

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73 views4 pages

Standard-Form Categorical Syllogisms Syllogism

Categorical syllogisms are deductive arguments with three categorical propositions: two premises and a conclusion. They must be in standard form with the major premise first, then the minor premise, and conclusion last. The middle term appears in both premises but not the conclusion. There are 64 possible moods that a syllogism can take based on whether the propositions are universal or particular affirmatives, negatives, or indefinites. Validity depends on the syllogism's form, not the subject matter. Venn diagrams can help test whether a syllogism is valid or invalid.

Uploaded by

John Cheeky
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Categorical Syllogisms

CATEGORICAL SYLLOGISMS
Standard-Form Categorical Syllogisms

Syllogism

- Any deductive argument in which a conclusion is inferred from two premises


o A, E, I, and O propositions have:
 Two categorical propositions as premises
 One categorical proposition as a conclusion
- Common, clear, and readily testable

Categorical Syllogism

- A deductive argument consisting of 3 categorical propositions


o Contains exactly 3 terms
 Which occurs in exactly 2 of the propositions
- Standard form
o The form in which a syllogism is said to be when its premises and conclusion are all standard-from
categorical propositions (A, E, I, or O)
o Arranged in standard order:
 Major premise
 Minor premise
 Conclusion
o e.g.
 No heroes are cowards
 Some soldiers are cowards
 Therefore, some soldiers are not heroes
- Terms of syllogism
o Middle term
 Term that appears in both premises
 Not in conclusion
o Major premise
 Premise containing the major term
 Major term
 Predicate term of the conclusion
o Minor premise
 Premise containing the minor term
 Minor term
 Subject term of the conclusion
Categorical Syllogisms
- Mood
o Characterization of categorical syllogisms determined by the types of standard-form categorical
propositions (i.e. A, E, I, or O)
 Every syllogism has a mood
 64 possible moods
o e.g. AAA, AAI, AAE, …, OOO
- Figure of Syllogism
o The position of the middle term in the premises of a standard-form categorical syllogism
o Example:

 Analysis
 All P is M
 Some S is M
 ∴ Some S is P
 Where:
 P = predicate
 M = middle-term
 ∴ = Therefore
o To describe the form of a syllogism:
 Mood must be stated
 Figure is drawn out
o Syllogisms have 4 possible figures:
 The middle term may be the subject term of the major premise and the predicate term of the
minor premise; or
 The middle term may be the predicate term of both premises; or
 The middle term may be the subject term of both premises; or
 The middle term may be the predicate term of the major premise and the subject term of the
minor premise.
Categorical Syllogisms

Formal Nature of Syllogistic Arguments

Discriminating Valid Arguments from Invalid Arguments

- Essential in deductive logic


o Discriminating valid syllogisms from invalid ones
- Assumption
o Constituent propositions of a syllogism are all contingent
 None of those propositions is necessarily true or false
o Validity/invalidity of a syllogism depends on its form
 Valid syllogisms are valid by virtue of its form alone
- Example:
o AAA-1 (Barbara syllogism)
 All M is P
 All S is M
 ∴ All S is P
o This syllogism is valid regardless of subject matter
- Example 2:
o All Greeks are humans
o All Athenians are Greeks
o Therefore, All Athenians are humans
Categorical Syllogisms
Venn Diagram Technique for Testing Syllogisms

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